Physics - Semiconductors Question with Solution | TestHub

${\beta }_{dc}=\frac{{\alpha }_{dc}}{1-{\alpha }_{dc}} \Rightarrow \left(1-{\alpha }_{dc}\right)=\frac{{\alpha }_{dc}}{{\beta }_{dc}}$
$\frac{{\beta }_{dc}-{\alpha }_{dc}}{{\alpha }_{dc}\cdot {\beta }_{dc}}=\frac{{\beta }_{dc}\left(1-\frac{{\alpha }_{dc}}{{\beta }_{dc}}\right)}{{\alpha }_{dc}\cdot {\beta }_{dc}}$
$=\frac{1-\frac{{\alpha }_{dc}}{{\beta }_{dc}}}{{\alpha }_{dc}}=\frac{1-\left(1-{\alpha }_{dc}\right)}{{\alpha }_{dc}}$
$=\frac{1-1+{\alpha }_{dc}}{{\alpha }_{dc}}=1$